Consider a reform that changed welfare benefits in New Jerse

Consider a reform that changed welfare benefits in New Jersey and suppose that at the same time there was no change in New York. The data for an average welfare recipients (per month) in the two states looks as follows: New Jersey New York Average hours of workAverage benefit Average hours of work Average benefit 1000 800 Before the reform 60 1000 After the reform (a) Explain what assumption(s) you need to make to rely on this data to estimate the effect of the reform. b) What is the difference-in-difference estimate of the effect of the reform on hours of work of welfare recipients? (c) What is the corresponding estimate on the effect on welfare benefits? (d) What is the implied elasticity of hours of work to the level of welfare benefits? (Note: Evaluate the elasticity using the initial point as a reference point.) 70 600 60

Solution

A reform has been taken and this changes the welfare benefits of New Jersy and it was also assume that at that time there was no change in New York. The data is showing for average welfare recipients.

a) The assumptions may require to rely on this data to know the effect of reform is -

i) Intervention or reform unrelated to outcome at baseline i.e allocation of reform is not determined by outcome

ii) Composition of reform are same in both place and the treatment groups of people i.e study groups are same before and after the reform

iii) No spillover effects due to the reform .

b) Difference - in - difference estimate of the effect of reform on hours of work of welfare recipients can be be measure by [(average hours of work at New Jersy post reform period - average hours of work at new jersy pre-reform period) - (average hours of work in New York post reform period - average hours of work pre-reform period)]

Here the treatment group is the welfare recipients of New Jersy and comparision group is welfare recipients of New York. To calculate difference-in-difference here the value for average working hours is [(70 - 60) - (60 -55)] = 10 - 5 = 5

c) Now the difference-in-difference estimate on welfare benefits is [(1000 - 600 ) - (800 - 600)] = 400 -200 =200

d) Now we will calculate the implied elasticity of hours of work to the level of welfare benefits. It means what is the change in hours of work due to change in welfare benefits. Here change in hours of work in New Jersy is 70 - 60 =10 and change in average benefit is 1000 - 600 = 400 . Therefore elasticity will be 10/400 * 60/1000 = 3/200